Typically, an ultrasound flow imaging system employs the conventional delay and sum (DAS) beamformer due to its inherent low complexity. But the conventional DAS technique offers poor contrast, low imaging resolution, and limited spatiotemporal sensitivity. This article attempts to improve the spatiotemporal sensitivity of conventional flow imaging with a novel multiply and sum based nonlinear high-resolution (NLHR) beamforming approach. The major advantages of the proposed beamformer are the harmonic generation and the enhanced coherence in beamformed signals that improve the spatiotemporal sensitivity towards flow transients. We demonstrate the proposed beamformer for a directional cross-correlation as well as an autocorrelation based velocity estimator with simulated parabolic flow profiles of different velocities and flow directions, an in-vitro rotating disk dataset, and pulsatile flow experiments. The sensitivity of NLHR beamforming towards the flow transients is validated in-vitro with a sudden reversal of flow direction and air bubble tracking experiments. The comparison between the time-frequency plots of DAS and NLHR beamforming indicates that the impulsive spatiotemporal changes induced by the flow of air bubbles are clearly characterized by nonlinear beamforming than that of DAS beamforming. Furthermore, better spatiotemporal velocity tracking of a single air bubble and a clear distinguishability between the tracking of two proximal air bubbles are observed in-vitro. Preliminary studies on the in-vivo carotid data also show comparable, if not better, results than that of the DAS algorithm. Detailed results for each test case in simulation, phantom, and in-vivo studies are available as movies with the supplementary material and online.